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A300647
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Number of same-trees of weight n in which all outdegrees are odd.
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6
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1, 1, 2, 1, 2, 2, 2, 1, 10, 2, 2, 2, 2, 2, 42, 1, 2, 10, 2, 2, 138, 2, 2, 2, 34, 2, 1514, 2, 2, 42, 2, 1, 2058, 2, 162, 10, 2, 2, 8202, 2, 2, 138, 2, 2, 207370, 2, 2, 2, 130, 34, 131082, 2, 2, 1514, 2082, 2, 524298, 2, 2, 42, 2, 2, 14725738, 1, 8226, 2058, 2
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OFFSET
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1,3
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COMMENTS
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A same-tree of weight n > 0 is either a single node of weight n, or a finite sequence of two or more same-trees whose weights are all equal and sum to n.
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LINKS
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FORMULA
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a(n) = 1 + Sum_d a(n/d)^d where the sum is over odd divisors of n greater than 1.
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EXAMPLE
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The a(9) = 10 odd same-trees:
9,
(333),
(33(111)), (3(111)3), ((111)33)
(3(111)(111)), ((111)3(111)), ((111)(111)3),
((111)(111)(111)), (111111111).
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MATHEMATICA
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a[n_]:=1+Sum[a[n/d]^d, {d, Select[Rest[Divisors[n]], OddQ]}];
Array[a, 80]
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PROG
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(PARI) a(n) = if (n==1, 1, 1+sumdiv(n, d, if ((d > 1) && (d % 2), a(n/d)^d))); \\ Michel Marcus, Mar 10 2018
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CROSSREFS
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Cf. A003238, A006241, A063834, A069283, A273873, A281145, A289078, A289079, A289501, A298118, A300436, A300439, A300574, A300648, A300649, A300650.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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